Volatility measurements using intra-daily data were first adopted by [1]} for the estimation of the daily range. Since then the literature has significantly expanded: from the realized volatility of [2]} and [3]} to realized
kernels of [4]} and realized covariance matrices [5]}, [6]}, [7]}. In parallel to
the evolution of these measures, there has been a natural complementary
effort to build adequate models to describe their dynamics. Multiplicative
Error Models have been used for this purpose for example by [8]}.
The time series which are most commonly used in this respect are the
squared close-to-close adjusted returns \(r_{t}^{2}\) , the realized
variances \(rv_{t}^{2}\)  (in any of their flavours), the absolute returns
\(\left|r_{t}\right|\) , the realized volatilities \(rv_{t}\) , and the
daily ranges \(hl_{t}\) . We will now illustrate the characteristics
of our DPMLN2-vMEM with
\(\mathbf {\mu }_{t}=\mathbf {\omega }+\mathbf {\beta }\mathbf {\mu }_{t-1}+\mathbf {A}\mathbf {x}_{t-1}\) 
